Tools

"... Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as time-varying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over ..."

Macroeconomic practitioners frequently work with multivariate time series models such as VARs, factor augmented VARs as well as time-varying parameter versions of these models (including variants with multivariate stochastic volatility). These models have a large number of parameters and, thus, over-parameterization problems may arise. Bayesian methods have become increasingly popular as a way of overcoming these problems. In this monograph, we discuss VARs, factor augmented VARs and time-varying parameter extensions and show how Bayesian inference proceeds. Apart from the simplest of VARs, Bayesian inference requires the use of Markov chain Monte Carlo methods developed for state space models and we describe these algorithms. The focus is on the empirical macroeconomist and we offer advice on how to use these models and methods in practice and include empirical illustrations. A website provides Matlab code for carrying out Bayesian inference in these models.

...use econometric modelling. For instance, Bayesian estimation of dynamic stochastic general equilibrium (DSGE) models is very popular. There will be no discussion of DSGE models in this monograph (see =-=An and Schorfheide, 2007-=- or Del Negro and Schorfheide, 2009 for excellent treatments of Bayesian DSGE methods). Also, macroeconomic theory is often used to provide identifying restrictions to turn reduced form VARs into stru...

"... Inference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely to appear in smaller models. Our framework allows for many regimes in the transition matrix, without letting the number of free parameters grow as the square as the number of regimes, but also witho ..."

Inference for multiple-equation Markov-chain models raises a number of difficulties that are unlikely to appear in smaller models. Our framework allows for many regimes in the transition matrix, without letting the number of free parameters grow as the square as the number of regimes, but also without losing a convenient form for the posterior distribution. Calculation of marginal data densities is difficult in these high-dimensional models. This paper gives methods to overcome these difficulties and explains why existing methods are unreliable. It makes suggestions for maximizing posterior density and initiating MCMC simulations that provide robustness against the complex likelihood shape. JEL: C32; C52; E4. Key words: Density overlap; new MHM; incremental and discontinuous changes;

... of the marginal distribution of a particular block of θ (see Sims and Zha (2004) for further details). For these reasons, this method has been found to be less reliable than the standard MHM method (=-=An and Schorfheide, 2007-=-; Justiniano and Primiceri, ming). To see how our methods are applied to estimation of the set of empirical models, we break θ further into several subblocks, one consisting of bj(k) for k = 1, . . . ...

"... A&M University for helpful comments. This research was conducted while Schorfheide was visiting the FRB Philadelphia, for whose hospitality he is thankful. Schorfheide gratefully acknowledges financial support ..."

A&amp;M University for helpful comments. This research was conducted while Schorfheide was visiting the FRB Philadelphia, for whose hospitality he is thankful. Schorfheide gratefully acknowledges financial support

"... Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumptio ..."

Importance sampling is used in many areas of modern econometrics to approximate unsolvable integrals. Its reliable use requires the sampler to possess a variance, for this guarantees a square root speed of convergence and asymptotic normality of the estimator of the integral. However, this assumption is seldom checked. In this paper we use extreme value theory to empirically assess the appropriateness of this assumption. Our main application is the stochastic volatility model, where importance sampling is commonly used for maximum likelihood estimation of the parameters of the model.

"... FEDERAL RESERVE BANK OF CLEVELANDWorking papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of ..."

FEDERAL RESERVE BANK OF CLEVELANDWorking papers of the Federal Reserve Bank of Cleveland are preliminary materials circulated to stimulate discussion and critical comment on research in progress. They may not have been subject to the formal editorial review accorded official Federal Reserve Bank of Cleveland publications. The views stated herein are those of the authors and are not necessarily those of the Federal Reserve Bank of Cleveland or of

"... This paper uses a general equilibrium DSGE model to estimate the SARB´s policy reaction rule. We nd that the SARB has a stable rule very much in line with those estimated for Canada, UK, Australia and New Zealand. Relative to other emerging economies the policy reaction function of the SARB appears ..."

This paper uses a general equilibrium DSGE model to estimate the SARB´s policy reaction rule. We nd that the SARB has a stable rule very much in line with those estimated for Canada, UK, Australia and New Zealand. Relative to other emerging economies the policy reaction function of the SARB appears to be much more stable with a consistent antiination bias, a somewhat larger weight on output and a very low weight on the exchange rate. Acknowledgement 1 Some of this material has been taken from joint work with Ernesto Talvi. We thank Thomas Lubik and Frank Schorfheide for sharing their codes and Pablo Glüzmann for outstanding research as-sistantship. This is part of the Government of South Africa ´ s joint project with Harvard University to discuss the binding constraints to growth for the economy. 1

"... This paper undertakes a Bayesian analysis of optimal monetary policy for the U.K. We estimate a suite of monetary-policy models that include both forwardand backward-looking representations as well as large- and small-scale models. We find an optimal simple Taylor-type rule that accounts for both mo ..."

This paper undertakes a Bayesian analysis of optimal monetary policy for the U.K. We estimate a suite of monetary-policy models that include both forwardand backward-looking representations as well as large- and small-scale models. We find an optimal simple Taylor-type rule that accounts for both model and parameter uncertainty. For the most part, backward-looking models are highly fault tolerant with respect to policies optimized for forward-looking representations, while forward-looking models have low fault tolerance with respect to policies optimized for backward-looking representations. In addition, backward-looking models often have lower posterior probabilities than forwardlooking models. Bayesian policies therefore have characteristics suitable for inflation and output stabilization in forward-looking models. 1

"... This paper estimates a two-country model with a global bank, using US and Euro Area (EA) data, and Bayesian methods. The estimated model matches key US and EA business cycle statistics. Empirically, a model version with a bank capital requirement outperforms a structure without such a constraint. A ..."

This paper estimates a two-country model with a global bank, using US and Euro Area (EA) data, and Bayesian methods. The estimated model matches key US and EA business cycle statistics. Empirically, a model version with a bank capital requirement outperforms a structure without such a constraint. A loan loss originating in one country triggers a global output reduction. Banking shocks matter more for EA macro variables than for US real activity. Banking shocks account for 2%-5 % of the unconditional variance of US GDP and for 4%-15 % of the variance of EA GDP. During the Great Recession (2007-09), banking shocks accounted for about 12-20 % of the fall in US and EA GDP, and for more than a third of the fall in EA investment and employment.